SPATIAL AND TIME-DEPENDENT REACTOR KINETICS METHODOLOGY BASED ON THE METHOD OF CHARACTERISTICS

摘要

A new approach based on the method of characteristics (MOC) and Rosenbrock method is developed to solve the time-dependent transport equation in one-dimensional (ID) geometry considering delayed neutron without any approximation. Using the MOC and newly developed exponential correlation, the ID time-dependent transport equation is decomposed into a series of locally coupled ordinary differential equations (ODE). In the set of ODE, the angular flux is coupled with all other angular flux and delayed neutron precursor densities in the same zone and in the previous zone along the neutron trajectories. Rosenbrock method is used to solve the system of ODEs; it is a fourth order explicit method with automatic step size control feature developed for stiff ODEs. The FORTRAN90 numerical program was developed to "translate" this complex and detailed kinetics model in solving the time-dependent transport equation considering delayed neutrons in ID geometry with both vacuum and reflective boundary conditions. The step and ramp perturbations are firstly selected to benchmark the new methodology. Based on two comprehensive benchmarks (a fast reactor with step perturbation and a thermal reactor with ramp perturbation), the developed numerical methodology was verified showing excellent accuracy and computational efficiency. This methodology is being developed for multi-dimensional arbitrary geometries. This paper presents the first results toward 3D kinetics methodology to be applied to pebble bed reactor (PBR) core.